Finite Group Databasebeta

← #29574962

Subgroups — #29574962

Order 15616.

416 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456164C211yesmaximal, characteristic
2#21444481C211yesmaximal, characteristic
3#21444291C212yesmaximal, complemented
4#21443717C212yesmaximal, complemented
5C61×#2980C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16840130—21no—
8#16840126—21no—
9#16840121C414yes—
10#16839815C2212yes—
11#16839758—22no—
12C2×#14519688C2211yescharacteristic
13#16839511—21no—
14#16839506—21no—
15#16839492—24no—
16C61×#532C2211yescharacteristic
17C61×#435—24no—
18C61×#432C2212yes—
19C61×#408—22no—
20C22×#92418—21no—
21#14519777C2×C412yes—
22#14519769—21no—
23#14519756—22no—
24C4×Dic122—22no—
25#14519736—21no—
26C4⋊#92418—22no—
27#14519701—24no—
28#14519698—24no—
29C22⋊#92418—22no—
30#14519688—21no—
31#14519688C2×C412yes—
32C4×#92418—22no—
33C2×#41×C61D412yes—
34C2×M16×C61—22no—
35C22×C8×C61—22no—
36C4⋊Q8×C61D411yescharacteristic
37#127×C61D411yescharacteristic
38#124×C61C2×C412yes—
39#121×C61—22no—
40C4×D4×C61—22no—
41C2×C42×C61C2311yescharacteristic
42C4⋊C8×C61D414yes—
43C22⋊C8×C61—24no—
44C22⋊C8×C61—22no—
45#97×C61—22no—
46#41×C61—42no—
47#41×C61—42no—
48C2×Q8×C61C22⋊C412yes—
49C2×D4×C61—22no—
50C2×D4×C61—22no—
51C2×D4×C61C22⋊C412yes—
52C22×C4×C61—22no—
53C22×C4×C61C2×D411yescharacteristic
54C22×C4×C61#4112yes—
55C2×Dic122—22no—
56M16×C61—82no—
57C2×C8×C61—24no—
58C2×C8×C61—82no—
59C4⋊C4×C61—22no—
60C22⋊C4×C61—24no—
61C42×C61C22×C411yescharacteristic
62C42×C61C2×D411yescharacteristic
63C42×C61C2×D412yes—
64C22⋊Dic61—41no—
65C4⋊Dic61—22no—
66C4⋊Dic61—22no—
67#11758196—42no—
68C4×Dic61—41no—
69C2×#92418—22no—
70C2×#92418—42no—
71C2×#92418—42no—
72C23×C61—22no—
73C23×C61#12311yescharacteristic
74Q8×C61—42no—
75D4×C61—42no—
76D4×C61—82no—
77D4×C61—82no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—42no—
81C2×C4×C61—42no—
82C2×C4×C61—42no—
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C2×C4×C61C4×D412yes—
85C2×C4×C61#12011yescharacteristic
86C2×C4×C61#12112yes—
87C2×Dic61—42no—
88Dic122—44no—
89C8×C61—44no—
90#92418—42no—
91#92418—82no—
92#9005—611nomaximal, Sylow
93C22×C61—22no—
94C22×C61—21no—
95C22×C61—44no—
96C22×C61—42no—
97C22×C61#38611yescharacteristic
98C4×C61—22no—
99C4×C61—22no—
100C4×C61—21no—
101C4×C61—42no—
102C4×C61#45512yes—
103Dic61—82no—
104#3135—611no—
105#2980D6111yescharacteristic
106#1543—611no—
107#1497—612no—
108#1302—612no—
109C2×C61—41no—
110C2×C61—82no—
111C2×C61#188112yes—
112C2×C61#188511yescharacteristic
113#533—611no—
114#532C2×D6111yescharacteristic
115#491—1221no—
116#490—1221no—
117#489—614no—
118#435—24no—
119#432C2×D6112yes—
120#431—612no—
121#416—1222no—
122#408—22no—
123C2×#97—611no—
124#333—1221no—
125#331—1221no—
126Q8⋊C8—1224no—
127C61#900511yescharacteristic, complemented, Sylow
128C2×#41C22⋊D6112yes—
129C2×M16—22no—
130C22×C8—22no—
131C22×C8—1221no—
132C4⋊Q8—612no—
133C4⋊Q8D24411yescharacteristic
134#127D24411yescharacteristic
135#125—1221no—
136#124C4×D6112yes—
137C22⋊Q8—1222no—
138#121—22no—
139C4×Q8—1222no—
140C4×D4—22no—
141#117—1221no—
142C2×C42C22×D6111yescharacteristic
143C4⋊C8—1222no—
144C4⋊C8C22⋊D6114yes—
145#103—1224no—
146#102—1224no—
147C22⋊C8—24no—
148C22⋊C8—22no—
149C22⋊C8—1222no—
150#97—22no—
151#97—612no—
152#97—1221no—
153C4×C8—1222no—
154#41—42no—
155#41—42no—
156C2×Q8—1222no—
157C2×Q8#1175819812yes—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4#1175819812yes—
161C22×C4—22no—
162C22×C4#1175822212yes—
163C22×C4C2×C22⋊D6111yescharacteristic
164M16—82no—
165C2×C8—24no—
166C2×C8—82no—
167C2×C8—1222no—
168C2×C8—2442no—
169C2×C8—2442no—
170C4⋊C4—22no—
171C4⋊C4—1222no—
172C4⋊C4—1222no—
173C4⋊C4—2442no—
174C22⋊C4—24no—
175C22⋊C4—2441no—
176C42—2441no—
177C42C2×C4×D6111yescharacteristic
178C42C2×D24411yescharacteristic
179C42C2×C22⋊D6112yes—
180C23—22no—
181C23#1451976011yescharacteristic
182Q8—42no—
183Q8—2444no—
184D4—42no—
185D4—82no—
186D4—82no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—2442no—
193C2×C4C2×#1175819811yescharacteristic
194C2×C4C4×C22⋊D6112yes—
195C2×C4#1451974611yescharacteristic
196C2×C4#1451975112yes—
197C8—44no—
198C8—4882no—
199C8—2442no—
200C22—22no—
201C22—21no—
202C22—44no—
203C22—42no—
204C22#1683964111yescharacteristic
205C4—22no—
206C4—22no—
207C4—21no—
208C4—42no—
209C4—4882no—
210C4#1683994012yes—
211C2—41no—
212C2—82no—
213C2#2144618112yes—
214C2#2144620711yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2980C2
socleC22×C61#386
prime radicalC61×#532C22
cosocleC2×C42×C61C23
hypercenter#2980D61
hypocenterC61#9005
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2980

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #21444291C2semidirect
4. #21443717C2semidirect
127. C61#9005semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214561642
#214444812
#214442912
#214437172
C61×#29802
#900561